Shouldn't Worf have waited until they met General Martok (,i.e. the real one in the Gamma Quadrant) and both would have had their names restored?
That supposes that Worf can see the future and knows that he'll meet Martok and they'll get on well enough for him to be invited into Martok's house.
I never understood why the House of Mogh was discredited anyhow in WOTW, didn't Worf and Kurn help Gowron become Chancellor?
As the songs says, "what have you done for me lately?"
Plus they got their gift for helping Gowron already, he reinstated their house and clear up the false accusations that Mogh assisted the Romulans in the attack on Khitomer. I'm sure Gowron would (maybe even most Klingons) consider that honour was satisfied already. So Worf was "obligated" to follow Gowron and that what Gowron did was justified.